Until 2017, the best known upper bound on the reset threshold was \((n^3-n)/6-1 \sim 0.1666\ldots n^3 + \mathcal {O}(n^2)\)  (\(n \ge 4)\)  [1]} by the well-known Frankl-Pin's bound.
The current best known upper bound is \(\sim 0.1654 n^3 + o(n^3)\)  by Shitov [2]}, which was obtained by refining the previous improvement \(\sim 0.1664 n^3 + \mathcal {O}(n^2)\)  by Szykuła [3]}.
Apart from that, better bounds were obtained for many special subclasses of automata.
Synchronizing automata are also applied in other theoretical areas, e.g., matrix theory [4]}, theory of codes [5]}, Markov processes [6]}.
Several new results around the topic appear every year.
Recently, a special journal issue was dedicated to the problem [7]} for the occasion of the 50th anniversary of the problem.
